OP, why do you think they would bring their kids? Do they have previous form on this?
Agree with BigBadMummy - get your DP to phone or speak in person with his mate, and say "we're really sorry we can't include children, but it's a small private dinner for 20 adults and the no-children rule applies to all. I hope that's ok, can you sort out a babysitter all right?"
Then if there is any hmm-ing about the problems of babysitters, DP can say "I'm really sorry to hear that. Can you let us know by xx date if you've been able to find someone, as we'll need to let the venue know if you can't come / we'd like to invite someone else if you can't make it." Then make sure DP calls back on that date, just to check they are sorted.
You might actually do this for everyone who has children - I did this for my wedding, not that many people had kids then, but I did ring people in person and explain why and check that they were ok to sort a sitter. They were all delighted to have the excuse of a night off to let their hair down!
Also, if this is the case, you can always talk it up a bit about wanting to have nice grown up food, lots to drink etc and that it just isn't suitable for kids. Won't it be great for everyone to kick back and have the night off etc etc ..